I. Field of the Invention
This invention relates to guided-mode resonance filters for producing narrowband optical radiation.
II. Description of Relevant Art
Methods of dispersing wave energy are known in the art. In particular, periodic elements, such as gratings, have been used to diffract wave energy, e g., such as light incident on the element. Diffraction gratings can be used to influence the amplitude, phase, direction, polarization, spectral composition, and energy distribution of a beam of light. Examples of classical applications of gratings include deflection, coupling, filtering, multiplexing, guidance, and modulation of optical beams in areas such as holography, integrated optics, optical communications, acousto-optics, nonlinear optics, and spectroscopy.
When light is incident on the ruled surface of a diffraction grating, it may be reflected (or backward diffracted) and transmitted (or forward diffracted) at angles that depend upon the spacing between the grooves of the grating, the angle of incidence, and the wavelength of the light. By the process of diffraction, light can be separated into its component wavelengths thereby forming a spectrum that can be observed, photographed, or scanned photoelectrically or thermoelectrically. Gratings are therefore used in common instruments such as spectroscopes, spectrometers, and spectrographs.
For gratings to be of practical use as filtering elements and for other applications, it is necessary to accurately predict the passband frequencies for the diffracted spectrum of output waves. Thus, accurate modeling analysis must be performed upon each specific grating in order to determine its diffraction efficiency at various incident wavelengths as well as with respect to other physical parameters. Diffraction efficiency, defined as the diffracted power of a given order divided by the input power, is optimally one (1) or 100% for a lossless diffraction filter grating. However, diffraction efficiency for the reflected wave can be maximized at a different wavelength than that of the transmitted wave. Accordingly, it is necessary to determine the maximum efficiencies and passband for both the reflected wave and the transmitted wave emanating from and through the grating.
In order to predict passband efficiencies, numerous modeling techniques have been attempted. In general, the efficiency of a grating varies smoothly from one wavelength to another. However, there can be localized troughs or ridges in the efficiency curve and these are observed as rapid variations of efficiency with a small change in either wavelength or angle of incidence. These troughs or ridges are sometimes called "anomalies". From the point of view of a spectroscopist, anomalies are a nuisance because they introduce spurious peaks and troughs into the observed spectrum. It is, therefore, very important that the positions and shapes of the anomalies be accurately predicted as well as the conditions under which they appear. Accordingly, previous modeling techniques have attempted to predict the position, magnitude, etc. of various anomalies which exist in diffraction gratings. A good overview of anomalies and their characteristics for optical reflection gratings is provided by A. Hessel and A. Oliner, "A New Theory of Wood's Anomalies on Optical Gratings," Applied Optics, Vol. 4, No. 10, pp. 1275-1297 (October, 1965).
Recently, there have been increased efforts to accurately predict this natural phenomenon called anomalies. As Hessel and Oliner point out, there are basically two types of anomalous effects. First, there is a Rayleigh type effect due to one of the spectral orders appearing at the grazing angle. Thus, anomalies occur when an order "passes off" over the grating horizon when, e.g., the angle of refraction is 90.degree.. Thus, at the wavelength at which an order is grazing the surface, or the so-called Rayleigh wavelength, there is a discontinuity in the number of orders that are allowed to propagate. The energy that is in the order which "passes off" has to be redistributed among the other orders and this accounts for the sudden fluctuations in the efficiency of these orders. Thus, an explanation exists for describing the position of the anomalies existing due to the Rayleigh effect. The second type of anomalous effect deals with a resonance-type effect caused by possible guided waves supported by the grating. This second form of anomaly depends upon the parameters of the grating, i.e. its thickness, permittivity, grating period, and also upon the wavelength and angle of incidence, etc. of the light wave as in the Rayleigh effect.
This secondary effect, dubbed "resonance effect" was studied by Hessel and Oliner. They presented calculated results for reflection gratings which accurately predicted the diffraction efficiency. However, the gratings previously studied were generally planar reflection gratings with the periodic structure modeled as a grating surface reactance function. They did not contain dielectric surface structures and/or transmissive structures added for support of a relatively thin grating element. A large commercial market currently exists for thin dielectric diffraction gratings, or diffraction gratings which can be placed on a semiconductor surface adjacent a semiconductor laser.
In order to make diffraction gratings acceptable for commercial markets, it is essential that an exact electromagnetic model be utilized in order to fully characterize the anomaly phenomenon. Simplified theories, used for many years, cannot describe resonance filtering characteristics of devices such as guided-mode resonance filters. In M. Moharam and T. Gaylord, "Rigorous Coupled-Wave Analysis of Planar-Grating Diffraction," Journal of the Optical Society of America, Vol. 71, No. 7, pp. 811-818, (July, 1981), a rigorous coupled-wave approach was used to model slanted gratings. As recently discovered , rigorous coupled-wave analysis also allows for accurate prediction of the anomalies solvable by equations formulated into a simple matrix form. A computer can thereby be used to provide an exact and rigorous prediction of anomalies based upon both the first and second types of anomalous effects. See, e.g., S.S. Wang, et al., "Guided-Mode Resonances in Planar Dielectric-Layer Diffraction Gratings," Journal of the Optical Society of America, A, Vol. 7, No. 8, pp. 1470-1474, (August, 1990).
Rigorous coupled-wave analysis provides an exact prediction of the location and magnitude of each anomaly and can, therefore, be used to model the guided-mode resonance filters for practical applications. S.S. Wang et al. article describes the rigorous coupled-wave analysis, but along with the Moharam and Gaylord reference cited above, S. S. Wang et al. does not disclose a guided-mode resonance filter.